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Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations

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  • Tauchen, George

Abstract

This article presents a solution algorithm for the capital growth model. The algorithm uses value-function iterations on a discrete state space. The quadrature method is used to set the grid for the exogenous process, and a simple equispaced scheme in logarithms is used to set the grid for the endogenous capital process. The algorithm can produce a solution to within four-digit accuracy using a state space composed of 1,800 points in total.

Suggested Citation

  • Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
    • Handle: RePEc:bes:jnlbes:v:8:y:1990:i:1:p:49-51
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    Cited by:

    1. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    2. Tarik Ocaktan & Michel Juillard, 2008. "Méthodes de simulation des modèles stochastiques d'équilibre général," Économie et Prévision, Programme National Persée, vol. 183(2), pages 115-126.
    3. Maldonado, Wilfredo L. & Svaiter, B.F., 2007. "Holder continuity of the policy function approximation in the value function approximation," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 629-639, June.
    4. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 185-206, May.
    5. Golombek, Rolf & Raknerud, Arvid, 2018. "Exit dynamics of start-up firms: Structural estimation using indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 204-225.
    6. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    7. John Rust, 1997. "A Comparison of Policy Iteration Methods for Solving Continuous-State, Infinite-Horizon Markovian Decision Problems Using Random, Quasi-random, and Deterministic Discretizations," Computational Economics 9704001, University Library of Munich, Germany.
    8. Kelly, David L. & Kolstad, Charles D., 1999. "Bayesian learning, growth, and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 491-518, February.
    9. Yuanyuan Chen & Stuart Fowler, 2016. "Hybrid Perturbation-Projection Method for Solving DSGE Asset Pricing Models," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 649-667, December.
    10. Duffy, John & McNelis, Paul D., 2001. "Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1273-1303, September.
    11. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2002. "An approximation algorithm for optimal consumption/investment problems," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 55-69, April.
    12. Peter Woehrmann & Willi Semmler & Martin Lettau, "undated". "Nonparametric Estimation of the Time-varying Sharpe Ratio in Dynamic Asset Pricing Models," IEW - Working Papers 225, Institute for Empirical Research in Economics - University of Zurich.
    13. Gamba, Andrea & Tesser, Matteo, 2009. "Structural estimation of real options models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 798-816, April.
    14. Kenneth L. Judd, 1991. "Minimum weighted residual methods for solving aggregate growth models," Discussion Paper / Institute for Empirical Macroeconomics 49, Federal Reserve Bank of Minneapolis.
    15. Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    16. Zhu, Junjun & Xie, Shiyu, 2011. "Asymmetric Shocks, Long-term Bonds and Sovereign Default," MPRA Paper 28236, University Library of Munich, Germany.

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